Explanation

tan 45° = 1 in trigonometry.

Explanation

The value of log 1, regardless of the base (as long as it's a valid base for logarithms,i.e., positive and not equal to 1), is always 0.

This is because any number raised to the power of 0 equals 1.

For example, log₁₀(1) = 0 and ln(1) = 0. 

Explanation

Given:  

x² − x = 12  

y² − y = 12  

So both equations are equal:  

x² − x = y² − y  

⇒ x² − x − y² + y = 0  

⇒ (x² − y²) − (x − y) = 0  

⇒ (x − y)(x + y − 1) = 0  

Now set each factor to zero:  

1. x − y = 0 → ⇒ x = y  

2. x + y − 1 = 0 → ⇒ x + y = 1

Now plug into original equation to find values:

Try solving x² − x = 12  

⇒ x² − x − 12 = 0  

⇒ (x − 4)(x + 3) = 0  

⇒ x = 4 or x = -3

Case 1: x = 4  

If x + y = 1 ⇒ y = -3  

Then x − y = 4 − (−3) = 7

Case 2: x = -3  

If x + y = 1 ⇒ y = 4  

Then x − y = -3 − 4 = −7

So possible values of x − y = 0 or ±7

Explanation

5x - 4 = 4x - 4  

Value of x

Solution:

Subtract 4x from both sides:  

5x - 4x - 4 = -4  

x - 4 = -4  

Add 4 to both sides:  

x = 0  

Explanation

To find the greatest prime factor of 87:

Step 1: Factorize 87

87 = 3 × 29

Step 2: Identify the prime factors  

- 3 is a prime number  

- 29 is a prime number

Explanation

- Cost of 1 egg = 60 ÷ 9 = Rs. 6.67

- Cost of 3 eggs = 6.67 × 3

= Rs. 20

Explanation

(7/8) × 96 = 84 

Explanation

- Start  

- Go 15 km North

- Turn West, go 10 km

- Turn South, go 5 km

- Turn East, go 10 km

Now check:

- North 15 km, then South 5 km → Net 10 km North

- West 10 km, then East 10 km → Net 0 km

So, final position is 10 km North of the starting point, and you're facing East (last direction moved).

Explanation

Let the son's present age = x  

Then father's age when son was born = x  

So current father's age = x + x = 2x  

Given father's age now = 36  

⇒ 2x = 36 → x = 18 (son's current age)  

5 years ago: 18 – 5 = 13

Explanation

If a person is at the same position from both ends:  

Total number of persons = (Position from one end) + (Position from other end) – 1  

= 19 + 19 – 1 = 37